Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}} = 2.76 TeV

Inclusive transverse momentum spectra of primary charged particles in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}}$ = 2.76 TeV have been measured by the ALICE Collaboration at the LHC. The data are presented for central and peripheral collisions, corresponding to 0-5% and 70-80% of the hadronic Pb-Pb cross section. The measured charged particle spectra in $|\eta|<0.8$ and $0.3 < p_T < 20$ GeV/$c$ are compared to the expectation in pp collisions at the same $\sqrt{s_{\rm NN}}$, scaled by the number of underlying nucleon-nucleon collisions. The comparison is expressed in terms of the nuclear modification factor $R_{\rm AA}$. The result indicates only weak medium effects ($R_{\rm AA} \approx$ 0.7) in peripheral collisions. In central collisions, $R_{\rm AA}$ reaches a minimum of about 0.14 at $p_{\rm T}=6$-7GeV/$c$ and increases significantly at larger $p_{\rm T}$. The measured suppression of high-$p_{\rm T}$ particles is stronger than that observed at lower collision energies, indicating that a very dense medium is formed in central Pb-Pb collisions at the LHC.Comment: 15 pages, 5 captioned figures, 3 tables, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/98

Two-pion Bose-Einstein correlations in central Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.Comment: 17 pages, 5 captioned figures, 1 table, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/388

Clostridium difficile isolates with increased sporulation: emergence of PCR ribotype 002 in Hong Kong

We identified a predominant clone of Clostridium difficile PCR ribotype 002, which was associated with an increased sporulation frequency. In 2009, 3,528 stool samples from 2,440 patients were tested for toxigenic C. difficile in a healthcare region in Hong Kong. A total of 345 toxigenic strains from 307 (13.3%) patients were found. Ribotype 002 was the predominant ribotype, which constituted 35 samples from 29 (9.4%) patients. The mean sporulation frequency of ribotype 002 was 20.2%, which was significantly higher than that of the 56 randomly selected ribotypes other than 002 as concurrent controls (3.7%, p < 0.001). Patients carrying toxigenic ribotype 002 were more frequently admitted from an elderly home (p = 0.01) and received more β-lactam antibiotics in the preceding 3 months compared with the controls (p = 0.04) . The identification of toxigenic ribotype 002 in 2009 was temporally related to a significant increase in both the incidence of toxigenic C. difficile from 0.53 to 0.95 per 1,000 admissions (p < 0.001) and the rate of positive detection from 4.17% to 6.28% (p < 0.001) between period 1 (2004–2008) and period 2 (2009). This finding should alert both the physician and the infection control team to the establishment of and possible outbreaks by ribotype 002 in our hospitals, as in the case of ribotype 027

Intronic Cis-Regulatory Modules Mediate Tissue-Specific and Microbial Control of angptl4/fiaf Transcription

The intestinal microbiota enhances dietary energy harvest leading to increased fat storage in adipose tissues. This effect is caused in part by the microbial suppression of intestinal epithelial expression of a circulating inhibitor of lipoprotein lipase called Angiopoietin-like 4 (Angptl4/Fiaf). To define the cis-regulatory mechanisms underlying intestine-specific and microbial control of Angptl4 transcription, we utilized the zebrafish system in which host regulatory DNA can be rapidly analyzed in a live, transparent, and gnotobiotic vertebrate. We found that zebrafish angptl4 is transcribed in multiple tissues including the liver, pancreatic islet, and intestinal epithelium, which is similar to its mammalian homologs. Zebrafish angptl4 is also specifically suppressed in the intestinal epithelium upon colonization with a microbiota. In vivo transgenic reporter assays identified discrete tissue-specific regulatory modules within angptl4 intron 3 sufficient to drive expression in the liver, pancreatic islet β-cells, or intestinal enterocytes. Comparative sequence analyses and heterologous functional assays of angptl4 intron 3 sequences from 12 teleost fish species revealed differential evolution of the islet and intestinal regulatory modules. High-resolution functional mapping and site-directed mutagenesis defined the minimal set of regulatory sequences required for intestinal activity. Strikingly, the microbiota suppressed the transcriptional activity of the intestine-specific regulatory module similar to the endogenous angptl4 gene. These results suggest that the microbiota might regulate host intestinal Angptl4 protein expression and peripheral fat storage by suppressing the activity of an intestine-specific transcriptional enhancer. This study provides a useful paradigm for understanding how microbial signals interact with tissue-specific regulatory networks to control the activity and evolution of host gene transcription

Systematic review with meta-analysis of the epidemiological evidence relating smoking to COPD, chronic bronchitis and emphysema

<p>Abstract</p> <p>Background</p> <p>Smoking is a known cause of the outcomes COPD, chronic bronchitis (CB) and emphysema, but no previous systematic review exists. We summarize evidence for various smoking indices.</p> <p>Methods</p> <p>Based on MEDLINE searches and other sources we obtained papers published to 2006 describing epidemiological studies relating incidence or prevalence of these outcomes to smoking. Studies in children or adolescents, or in populations at high respiratory disease risk or with co-existing diseases were excluded. Study-specific data were extracted on design, exposures and outcomes considered, and confounder adjustment. For each outcome RRs/ORs and 95% CIs were extracted for ever, current and ex smoking and various dose response indices, and meta-analyses and meta-regressions conducted to determine how relationships were modified by various study and RR characteristics.</p> <p>Results</p> <p>Of 218 studies identified, 133 provide data for COPD, 101 for CB and 28 for emphysema. RR estimates are markedly heterogeneous. Based on random-effects meta-analyses of most-adjusted RR/ORs, estimates are elevated for ever smoking (COPD 2.89, CI 2.63-3.17, n = 129 RRs; CB 2.69, 2.50-2.90, n = 114; emphysema 4.51, 3.38-6.02, n = 28), current smoking (COPD 3.51, 3.08-3.99; CB 3.41, 3.13-3.72; emphysema 4.87, 2.83-8.41) and ex smoking (COPD 2.35, 2.11-2.63; CB 1.63, 1.50-1.78; emphysema 3.52, 2.51-4.94). For COPD, RRs are higher for males, for studies conducted in North America, for cigarette smoking rather than any product smoking, and where the unexposed base is never smoking any product, and are markedly lower when asthma is included in the COPD definition. Variations by sex, continent, smoking product and unexposed group are in the same direction for CB, but less clearly demonstrated. For all outcomes RRs are higher when based on mortality, and for COPD are markedly lower when based on lung function. For all outcomes, risk increases with amount smoked and pack-years. Limited data show risk decreases with increasing starting age for COPD and CB and with increasing quitting duration for COPD. No clear relationship is seen with duration of smoking.</p> <p>Conclusions</p> <p>The results confirm and quantify the causal relationships with smoking.</p